Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension

htmlabstractWe construct an efficient classical analogue of the quantum matrix inversion algorithm [HHL09] for low-rank matrices. Inspired by recent work of Tang [Tan18a], assuming length-square sampling access to input data, we implement the pseudo-inverse of a low-rank matrix and sample from the solution to the problem Ax = b using fast sampling techniques. We implement the pseudo-inverse by finding an approximate singular value decomposition of A via subsampling, then inverting the singular values. In principle, the a